They were briefly displayed for Syrian and Iraqi officials on Sunday, although the museum itself remains closed to the public.
Officials said it was the largest mass return of artefacts since 2003, but that they hoped other countries in the region would follow Syria's lead.
Mohammad Abbas al-Oreibi, Iraq's acting state minister of tourism and archaeology, said he planned to visit Jordan soon to persuade its authorities to hand back more than 150 items.
The museum has in the past housed one of the world's greatest collections, and was particularly known for its Assyrian Hall, made up of stone panels from a royal palace.
The panels escaped being looted simply because they were too big to be carried away.
The UN cultural body Unesco said last month that between 3,000 and 7,000 items are still believed to be missing, including about 40 to 50 that are considered to be of great historic importance.
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